The Mathematical Foundations of the Potential Payback Period (PPP)

Rainsy Sam

MPRA Paper from University Library of Munich, Germany

Abstract: This paper presents the mathematical foundations of the Potential Payback Period (PPP) as a unified framework for asset valuation and return determination. The PPP integrates earnings growth, discounting, and risk into a single dynamic metric derived from exponential growth and present value theory. Using limit analysis (L’Hôpital’s rule and Taylor expansions), we show that the Price-to-Earnings (P/E) ratio emerges as a limiting case of the PPP. The framework further defines a closed-loop system in which terminal valuation and return are endogenously determined, enabling the construction of return measures comparable to bond yields.

Keywords: Potential Payback Period (PPP); Asset Valuation; Price-to-Earnings Ratio (P/E); Discounted Cash Flow; Exponential Growth; Present Value; Limit Theory; L’Hôpital’s Rule; Taylor Expansion; Internal Rate of Return (IRR); Closed-Loop Valuation; Equity–Bond Comparison (search for similar items in EconPapers)
JEL-codes: G1 G11 G12 (search for similar items in EconPapers)
Date: 2026-04-18
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